The phenomenon above was investigated extensively in the physics literature (see e.g. [1]}, [2]}, [3]}, [4]} and the references therein). It is similar to the one occurring in superconductivity and the solutions whose existence we establish are analogous to the superconducting Abrikosov vortex lattices ([5]}, see e.g. [6]}, for a review). It is estimated in [3]} that the spontaneous symmetry breaking take place at the critical average magnetic field of approximately \(10^{24}\)  Gauss \(=10^{20}\)  Tesla. By comparison, the strongest magnetic field produced on Earth is \(10^{14} \)  Tesla.
